Lecture 26 Laplace Transform for Circuit Analysis Hung-yi Lee

Reference Chapter 10.3

What are we considering? Complete Response Natural Response Forced Response Zero State Response Zero Input Response Transient Response Steady State Response Final target What really observed Chapter 6 Chapter 10 Laplace Transform

Laplace Transform for Circuit Analysis 現實 第 N 層夢境 小開有了不要繼 承父業的念頭 小開 ( 競爭對手 ) 解散公司 進入夢境 清醒 直接說服 小開 小開的父親說： "I'm disappointed that you're trying so hard to be me."

Laplace Transform for Circuit Analysis Circuit in time domain Circuit in s-domain Branch variables in s-domain Branch variables in time domain Laplace Transform Inverse Laplace Transform Differential Equation Node Analysis, Mesh Analysis, Thevenin, Norton Superposition ……

Resistor Laplace Transform

Voltage Source Laplace Transform

Current Source Laplace Transform

Capacitor Laplace Transform

Capacitor Laplace Transform

Capacitor Source Transformation Time Domain s-domain

Inductor Laplace Transform

Inductor Laplace Transform

Inductor Source Transformation Time Domain s-domain

Example 1 Laplace Transform

Example 1 Do inverse Laplace transform to find v o (t)

Example 1

Example 2 A B A B

Do inverse Laplace transform to find v C (t)

Example 2

Laplace v.s. Phasor (Chapter 13)(Chapter 6, 10)

Laplace v.s. Phasor Complete Response Natural Response Forced Response Zero State Response Zero Input Response Phasor method (chapter 10)

Natural Response from Zero Input If we set the initial conditions to be zero (zero-state) Reduce to generalized impedance

Natural Response from Zero State Example 13.11: Phasor

Natural Response from Zero State Example 13.11: Phasor

Natural Response from Zero State Example 13.11: Laplace transform Initial condition is all zero (zero state) Laplace Transform

Natural Response from Zero State Example 13.11: Laplace transform Natural Response

What actually happens in Chapter 10 and 11 Circuit, Filter Forced response Natural response (for zero state) The complex frequency corresponding to poles Natural response (for zero input) If the initial condition is not zero vanish eventually

Homework 13.51, 13.57, 13.58, 13.63, 13.65

Answer 13.51: y(t)=2-12te -3t +e -3t -3e -5t 13.57: y(t)= e -t cos(2t-26.6 。 ) 13.58: i1(t)=8e -4t – 2e -10t 13.63: v1(t)=23.6e 3t cos(4t-32.0 。 ) 13.65: VL(s)=20/(s 2 +14s+40), VL(0+)=0, VL’(0+)=20